TS EAMCET 4-Aug-2021 Shift 1 Question Paper

Let S1≡x2+y2+13x−3y=0 and
S2≡2x2+2y2+4x−7y−25=0
Equation of circle passing through point of intersection of S1 and S2 is given by
S1+λS2=0‌
(x2+y2+13x−3y)‌+λ(2x2+2y2
‌+4x−7y−25)=0 . . . (i)
This circle is passing through (1,1).
∴[12+12+13(1)−3(1)]+λ[2(1)22(1)2
‌+4(1)−7(1)−25]=0
From Eq. (i), we get
⇒λ=1∕2
4x2+4y2+30x−13y−25=0